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On Lp(T2)-Convergence and Móricz
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  • Journal title : Journal for History of Mathematics
  • Volume 28, Issue 6,  2015, pp.321-332
  • Publisher : The Korean Society for History of Mathematics
  • DOI : 10.14477/jhm.2015.28.6.321
 Title & Authors
On Lp(T2)-Convergence and Móricz
LEE, Jung Oh;
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 Abstract
This paper is concerned with the convergence of double trigonometric series and Fourier series. Since the beginning of the 20th century, many authors have studied on those series. Also, Ferenc has studied the convergence of double trigonometric series and double Fourier series so far. We consider -convergence results focused on the Ferenc studies from the second half of the 20th century up to now. In section 2, we reintroduce some of Ferenc remarkable theorems. Also we investigate his several important results. In conclusion, we investigate his research trends and the simple minor genealogy from J. B. Joseph Fourier to Ferenc . In addition, we present the research minor lineage of his study on -convergence.
 Keywords
double Fourier series;summability of double Fourier series;convergence of Fourier series;double trigonometric series;
 Language
Korean
 Cited by
 References
1.
Chang-Pao CHEN, Hui-Chuan WU, F. MORICZ, Pointwise convergence of multiple trigonometric series., J. Math. Anal. Appl. 185(3) (1994), 629-646. crossref(new window)

2.
X. Z. KRASNIQI, P. KORUS, F. MORICZ, Necessary conditions for the $L^p$-convergence (0 < p < 1) of single and double trigonometric series., Mathematica Bohemica 139(1) (2014), 75-88.

3.
L. KRIZSAN, F. MORICZ, The Lebesque summability of double triginometric integrals, Mathematical Inequalities & Applications 17(4) (2014), 1543-1550.

4.
LEE Jung Oh , A brief study on Bhatia's research of $L^1$-convergence, The Korean Journal for History of Mathematics 27(1) (2014), 81-93. crossref(new window)

5.
LEE Jung Oh, On Classical Studies for the Summability and Convergence of Double Fourier Series, The Korean Journal for History of Mathematics, 27(4) (2014), 285-297. crossref(new window)

6.
F. MORICZ, Convergence and integrability of double trigonometric series with coefficients of bounded variation, Proc. Am. Math. Soc.102(3) (1988), 633-640. crossref(new window)

7.
F. MORICZ, On the integrability of double cosine and sine series. I., J. Math. Anal. Appl. 154(2) (1991), 452-465. crossref(new window)

8.
F. MORICZ, On the integrability of double cosine and sine series. II., J. Math. Anal. Appl. 154(2) (1991), 466-483. crossref(new window)

9.
F. MORICZ, $L^1$-convergence of double Fourier series., Journal of Mathematical Analysis and Applications 186 (1994), 209-236. crossref(new window)

10.
F. MORICZ, On the maximal Fejer operator for double Fourier series of functions in Hardy spaces., Stud. Math. 116(1) (1995), 89-100. crossref(new window)

11.
F. MORICZ, Necessary conditions for $L^1$-convergence of double Fourier series, J. Math. Anal. Appl. 363 (2010), 559-568. crossref(new window)

12.
F. MORICZ, M. BAGOTA, On the Lebesgue summability of double trigonometric series, J. Math. Anal. Appl. 348 (2008), 555-561. crossref(new window)

13.
F. MORICZ, B. E. RHOADES, Approximation by Norlund means of double Fourier series for Lipschitz functions, J. Approximation Theory 50 (1987), 341-358. crossref(new window)

14.
F. MORICZ, Shi, Xianliang, Approximation to continuous functions by Cesaro means of double Fourier series and conjugate series, J. Approximation Theory 49 (1987), 346-377. crossref(new window)

15.
F. MORICZ, Daniel WATERMAN, Convergence of double Fourier series with coefficients of generalized bounded variation., J. Math. Anal. Appl. 140(1) (1989), 34-49. crossref(new window)